From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples

2025/06/23 by Euler, Marianna, Euler, Norbert · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2506.19070

Abstract

In this paper we derive two examples of fully-nonlinear symmetry-integrable evolution equations with algebraic nonlinearities, namely one class of 3rd-order equations and a 5th-order equation. To achieve this we study the equations' Lie-Bäcklund symmetries and apply multipotentialisations, hodograph transformations and generalised hodograph transformations to map the equations to known semilinear integrable evolution equations. As a result of this, we also obtain interesting symmetry-integrable quasilinear equations of order five and order seven, which we display explicitly.

Citations

• On differential equations invariant under a projective transformation group: integrability and reductions
• Recursion operators for a class of integrable third-order evolution equations

Cited by

• Two sequences of fully-nonlinear evolution equations and their symmetry properties

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